Geodesic
On global solvability of nonlinear equations with parameters
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 68-72

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We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions and to the problem of coincidence points of smooth and continuous compact mappings.
Keywords: global implicit function, implicit function extension, coincidence point. 
@article{DANMA_2021_496_a14,
     author = {A. V. Arutyunov and S. E. Zhukovskiy},
     title = {On global solvability of nonlinear equations with parameters},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {68--72},
     publisher = {mathdoc},
     volume = {496},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_496_a14/}
}
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A. V. Arutyunov; S. E. Zhukovskiy. On global solvability of nonlinear equations with parameters. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 68-72. http://geodesic.mathdoc.fr/item/DANMA_2021_496_a14/